This paper presents a new more general formulation of the algorithms for reduced order eigenanalysis of selective modal analysis. This formulation, instead of assuming an initial separation of the state variables for the modes of interest into relevant and less relevant ones, uses approximations of the corresponding right and left eigenvectors in the form of reduced order subspaces. The advantage of the proposed formulation is that the reduced order subspaces are updated in each step of the iterative process. The performance of the generalized selective modal analysis is illustrated in a large scale power system.